If you don’t need to specify the corners of the rectangle relatively, you can use a rectangle node for this.
The \pgfpointlineattime{<factor>}{<p1>}{<p2>} macro is the low-level PGF version of ($(<p1>)!<factor>!(<p2>)$) which is also used in the placement of nodes along a straight line with the pos=<factor> option.
If you want to add a specific padding length, you can use the fit library with inner xsep and inner ysep.
The backgrounds library is only used to add a simply grid to the picture.
Code
\documentclass[tikz]{standalone}
\usetikzlibrary{calc,backgrounds,fit}
\makeatletter
\tikzset{
from/.code args={#1 to #2}{%
\pgfextract@process\tikz@fromto@first{\tikz@scan@one@point\pgfutil@firstofone#1\relax}%
\pgfextract@process\tikz@fromto@second{\tikz@scan@one@point\pgfutil@firstofone#2\relax}%
% The next line sets "at".
\pgfextract@process\tikz@node@at
{\pgfpointlineattime{.5}{\tikz@fromto@first}{\tikz@fromto@second}}%
\pgfpointdiff{\tikz@fromto@first}{\tikz@fromto@second}%
\tikzset{
shape=rectangle,
anchor=center,
inner sep=+0pt,
outer sep=+0pt,
minimum width/.expanded={abs(\the\pgf@x)},
minimum height/.expanded={abs(\the\pgf@y)}}%
}
}
\makeatother
\begin{document}
\begin{tikzpicture}[gridded,nodes={orange, draw, fill, fill opacity=.5}]
\path (1,1) coordinate (a)
(3,4) coordinate (b)
(4,1) coordinate (a')
(6,4) coordinate (b');
\node[from=(a) to (b), xscale=1.1, yscale=1.05] {};
\node[fit=(a')(b'), inner xsep=.1cm, inner ysep=.07cm] {};
\end{tikzpicture}
\end{document}
Output

calclibrary withxscaleandyscalebut that does scale the coordinate, not the rectangle. The0,0coordinate would also be un-affected by this. There isscale aroundwhich you could use to scale around($(Q3term1)!.5!(Q3term2)$)but this works only for the same scale in both directions. Maybe it can be easier done with a node like in tikz: Can we set the corner coordinates of a rectangle? – Qrrbrbirlbel Aug 30 '13 at 03:31